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Simplifying 36x2 + -55x + 25 = 646 Reorder the terms: 25 + -55x + 36x2 = 646 Solving 25 + -55x + 36x2 = 646 Solving for variable 'x'. Reorder the terms: 25 + -646 + -55x + 36x2 = 646 + -646 Combine like terms: 25 + -646 = -621 -621 + -55x + 36x2 = 646 + -646 Combine like terms: 646 + -646 = 0 -621 + -55x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -17.25 + -1.527777778x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + -1.527777778x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + -1.527777778x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + -1.527777778x + x2 = 0 + 17.25 -1.527777778x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 -1.527777778x + x2 = 17.25 The x term is -1.527777778x. Take half its coefficient (-0.763888889). Square it (0.5835262347) and add it to both sides. Add '0.5835262347' to each side of the equation. -1.527777778x + 0.5835262347 + x2 = 17.25 + 0.5835262347 Reorder the terms: 0.5835262347 + -1.527777778x + x2 = 17.25 + 0.5835262347 Combine like terms: 17.25 + 0.5835262347 = 17.8335262347 0.5835262347 + -1.527777778x + x2 = 17.8335262347 Factor a perfect square on the left side: (x + -0.763888889)(x + -0.763888889) = 17.8335262347 Calculate the square root of the right side: 4.222975993 Break this problem into two subproblems by setting (x + -0.763888889) equal to 4.222975993 and -4.222975993.Subproblem 1
x + -0.763888889 = 4.222975993 Simplifying x + -0.763888889 = 4.222975993 Reorder the terms: -0.763888889 + x = 4.222975993 Solving -0.763888889 + x = 4.222975993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.763888889' to each side of the equation. -0.763888889 + 0.763888889 + x = 4.222975993 + 0.763888889 Combine like terms: -0.763888889 + 0.763888889 = 0.000000000 0.000000000 + x = 4.222975993 + 0.763888889 x = 4.222975993 + 0.763888889 Combine like terms: 4.222975993 + 0.763888889 = 4.986864882 x = 4.986864882 Simplifying x = 4.986864882Subproblem 2
x + -0.763888889 = -4.222975993 Simplifying x + -0.763888889 = -4.222975993 Reorder the terms: -0.763888889 + x = -4.222975993 Solving -0.763888889 + x = -4.222975993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.763888889' to each side of the equation. -0.763888889 + 0.763888889 + x = -4.222975993 + 0.763888889 Combine like terms: -0.763888889 + 0.763888889 = 0.000000000 0.000000000 + x = -4.222975993 + 0.763888889 x = -4.222975993 + 0.763888889 Combine like terms: -4.222975993 + 0.763888889 = -3.459087104 x = -3.459087104 Simplifying x = -3.459087104Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.986864882, -3.459087104}
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